Project Summary Fundamental challenges that hinder the current understanding of biomolecular systems are their tremendous complexity, high dimensionality and excessively large data sets associated with their geometric modeling and simulations. These challenges call for innovative strategies for handling massive biomolecular datasets. Topology, in contrast to geometry, provides a unique tool for dimensionality reduction and data simplification. However, traditional topology typically incurs with excessive reduction in geometric information. Persistent homology is a new branch of topology that is able to bridge traditional topology and geometry, but suffers from neglecting biological information. Built upon PI?s recent work in the topological data analysis of biomolecules, this project will explore how to integrate topological data analysis and machine learning to significantly improve the current state-of-the-art predictions of protein-ligand binding and mutation impact established in the PI?s preliminary studies. These improvements will be achieved through developing physics-embedded topological methodologies and advanced deep learning architectures for tackling heterogeneous biomolecular data sets arising from a variety of physical and biological considerations. Finally, the PI will establish robust databases and online servers for the proposed predictions.